Corollary 4

Tag 0D8B, permanent. Cite it as [Bourbaki, Tag 0D8B].

Commutative Algebra, chapter X, § 6. Extension des scalaires dans les algèbres régulières

Let $k$ be a field, $A$ a $k$ -algebra essentially of finite type, and $K$ an extension of $k$ which is a perfect field. In order that $A$ be absolutely regular (resp. absolutely normal), it is necessary and sufficient that the ring $A_{(K)}$ be regular (resp. normal).

This results from cor. 3 and example 1.

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

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